GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Sep 2018, 15:51

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Merry and Michelle play a card game. In the beginning

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
User avatar
Joined: 21 Oct 2013
Posts: 426
Merry and Michelle play a card game. In the beginning  [#permalink]

Show Tags

New post 06 Jun 2014, 13:41
1
5
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

73% (03:05) correct 27% (02:48) wrong based on 198 sessions

HideShow timer Statistics

Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54
Senior RC Moderator
User avatar
P
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 1180
Location: India
WE: General Management (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Merry and Michelle play a card game. In the beginning  [#permalink]

Show Tags

New post 06 Jun 2014, 23:53
3
We can use the plugging in method to solve this problem.

So straight away if we start plugging in option C = 36. We get the number of cards for merry as 45(after rounding off) and number of cards for Michelle as 27- The numbers are reflected after the 3rd game. This is not correct as Merry ends up having only 14 cards extra. In this case, it is more than 14. So Eliminate C, D and E.
Now we can try with B.





Number of Cards
GameMichelleMerry
Initially2727
After game 11836
After game 23024
After game 32034



Now Merry has 14 cards more than Michelle. This option gives us exactly what number of cards they had initially.

So the answer is B.
_________________

Become a GMAT Club Premium member to avail lot of discounts

Senior Manager
Senior Manager
avatar
Joined: 08 Apr 2012
Posts: 386
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

Show Tags

New post 07 Jun 2014, 09:17
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54

Anyone solving this with equations?
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 277
Premium Member
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

Show Tags

New post 07 Jun 2014, 09:51
1
1
ronr34 wrote:
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54

Anyone solving this with equations?


no. of cards after each round are shown in the following figure.

after round 3, merry have 14 more cards than michelle.
i.e. (34x/27)-(20x/27)=14

14x/27=14; x=27 hence B
Attachments

1.PNG
1.PNG [ 4.95 KiB | Viewed 2796 times ]

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

Show Tags

New post 07 Jun 2014, 10:19
1
ronr34 wrote:
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54


Anyone solving this with equations?


This question is a perfect candidate for plugging in the answer choices. Algebraic approach would be a waste of time.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
G
Joined: 14 Oct 2012
Posts: 174
Premium Member Reviews Badge
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

Show Tags

New post 17 Sep 2016, 14:16
My 2 cents:
This question can also be solved logically. We need a number which can be divided by 3, three times. Hence it MUST be a multiple of 27. Here 27 and 54 satisfy this condition. We can start with 27 and solve as Gnpth has done. Solving one will tell us which one is the answer.
Cheers!!!
Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1322
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

Show Tags

New post 11 Feb 2017, 07:05
1
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54


Official solution from The Economist.

Numbers in the answer choices and a specific question ("...how many cards...") call for Plugging In The Answers. If you feel like writing down equations, or if you are stunned by a long convoluted story in the question, stop! These are stop signs for Reverse PI.

Assume the amount in the answer choice is the number of cards each players has in the beginning, and then follow the story in the problem. If everything fits - stop. Pick it. Otherwise - POE and move on, until you find an answer that works.

First, plug in answer choice C. Assume that each player had 36 cards in the beginning of the game. This is how the game proceeds:
                                                                 Michelle      Mary       
Equal amounts                                             36            36
Michelle gives 1/3 · 36=12 cards to Mary        24            48
Mary gives 1/3 · 48=16 cards to Michelle        40            32
Michelle gives 1/3 · 40 cards to Mary         40-40/3     32+40/3

The last turn cannot be accomplished because a third of 40 cards is not an integer number. POE C, and look for another answer choice.
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/

Intern
Intern
avatar
B
Joined: 17 May 2017
Posts: 20
GMAT 1: 690 Q50 V33
WE: Analyst (Advertising and PR)
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

Show Tags

New post 17 May 2017, 04:58
raghavsatwik to know which is better that totally depends on your strength in which you are comfortable
Personally for me plugging in is more easy and simple
while algebric is waste of time
_________________

Mention why you eliminated each option
Thanks In Advance

Manager
Manager
User avatar
S
Joined: 02 Aug 2017
Posts: 69
Concentration: Strategy, Nonprofit
Schools: ISB '20
GPA: 3.71
Merry and Michelle play a card game. In the beginning  [#permalink]

Show Tags

New post 11 Aug 2018, 00:40
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54


Start with value 3 for both the cases, and make a table as shown in the picture. When you arrive at a stage in which you can't further divide a number by 3, multiply all values by 3. The value you get at the top is the correct answer :27

Posted from my mobile device
Attachments

15339732912034606703989131863871.jpg
15339732912034606703989131863871.jpg [ 2.14 MiB | Viewed 402 times ]


_________________


Everything is in flux, nothing stays still


MGMAT1 :590 Q42 V30 (07/07/18)
VERITAS :660 Q48 V33 (16/07/18)
GMATPREP1 :690 Q46 V36 (22/07/18)
GMATPREP2 :740 Q51 V39 (06/08/18)
ECONOMIST :740 Q49 V44 (11/08/18)
KAPLAN :690 Q49 V36 (17/08/18)
PRINCETON :690 Q48 V38 (26/08/18)
MGMAT2 :720 Q43 V45 (02/09/18)

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

Show Tags

New post 18 Aug 2018, 20:11
1
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54


Let x = the number of cards they each have at the beginning of the game.

After the first turn, i.e., after Michelle gives one-third of her cards (i.e., (1/3)x cards) to Merry, Michelle has x - (1/3)x = (2/3)x cards and Merry has x + (1/3)x = (4/3)x cards.

After the second turn, i.e., after Merry gives one-third of her cards (i.e., (1/3)(4/3)x = (4/9)x cards) to Michelle, Merry has (4/3)x - (4/9)x = (8/9)x cards and Michelle has (2/3)x + (4/9)x = (10/9)x cards.

After the third (or last) turn, i.e., after Michelle gives one-third of her cards (i.e., (1/3)(10/9)x = (10/27)x cards) to Merry, Michelle has (10/9)x - (10/27)x = (20/27)x cards and Merry has (8/9)x + (10/27)x = (34/27)x cards.

Since Merry ended up with 14 more cards than Michelle, we subtract the number of Michelle’s cards from the number of Merry’s cards, obtaining:

(34/27)x - (10/27)x = 14
(14/27)x = 14

x = 14 * (27/14)

x = 27

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: Merry and Michelle play a card game. In the beginning &nbs [#permalink] 18 Aug 2018, 20:11
Display posts from previous: Sort by

Merry and Michelle play a card game. In the beginning

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.